5 - The σ-Orientation

Summary

In this chapter, we bring the results of the preceding four chapters to bear on the problem of understanding String bordism, first using its lower–connectivity analogues and its complex analogue to paint a landscape into which these results naturally fit. Our overall strategy is again guided by the structure of the moduli of formal groups, which leads us to pursue a calculation of the Morava E–theory of complex bordism spectra before bringing us to the general topological results we seek. We conclude with a summary of unpublished results of Ando, Hopkins, and Strickland on the String–orientation of elliptic field spectra. We also include an extended discussion of elliptic curves, specialized to the context most relevant to us, for the reader’s convenience.